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$?~OOOZZZO7$+=:,,,..,.,...,.....,::~====~:::::,,,,,:::::~~~~~:~~=?7$OOO8$$$$$$$777$7777777777$7$$77I7I7I7=:,,,...,,,,,,::~~++I7$$Z$$$ZZ$$?~:,,,,,.,,,.........,,,,,,,:~+??77Z$Z$,,,.,..,,,,,:~I7ZD88DDDO
?+8O7OZZOOZ$I?=:,,,,,..,........,.,,,,,,,=:::::,,,,,,,,:::::,:===?IZOZOOZ777$77$777$7$77$$777$7$$$7777=::,,.....,,,,,:~~~=?II7$O$$ZZZZZ77?~:,,,~,,,,,,......,,,,,:,,:~==+I$7$Z~,,.......,,,::+I$888DDD8$
?I888OOOOZOO$?=~:,,,,,,,,..........,...,,.,,,,.,....,,,,,,,,,,:,::~+?$8O8777777$$7777$$$$7777$77$77+:,,.......,,:,,::=++?I77ZOZ$$$ZZ$ZZZ?~,::,=,,,:::,,,.,..,.,,:,::::~++?II:,........,,,,::~?7ZZ8888D8$
?=O8OIOOZ8OO7I?+=~~,,,,,,,,,....,,,,.,,,,,,,,........,,,,,,,,,,,,:~=+I+$8Z7I77?III?I?I777777777777=,,...,..,,,::::~+??777$$ZZ:7Z$ZZZ$7ZI,:::~::=7+=+,,,,,,.,,,,,,:,:,~~~+=:,..........,,,::~?I$ZODDDDD8$
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7+???++++===++I,II??+I+??I7+7???IIII????~III??III????~$I??I=III?I??III?I=I?:I7III?+II,+I??~7I:=~~:~??+?~7??+==++:~:=~,:~~:==+=++?~+??=~+~+?+=+?I???II777I7IIIII?777II7????++=~====~:+=:+,~?III+=?=+?~=++
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77I?????+~?=+?I==?II?+?+??I+IIIIIII??II+,I??????I????+II?I~?III?IIIII??:??+=I77?????++?+??+$?+~+:IO?+++~:$?++~+~:==~:==~:~=+==++++++I+==:+=?+=+??I???+??=?+=+?~=??II?+I~~+==+=+===,+:=+,~=?II===?=?+~==+
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???II??I?++~++?+=?III????I7??I?I?I?+???I.?II?II???+?+=+?+=??I???+I?I?I=??~:+?$II?I?+?I+??II7I??~IO?????????++=+~~====+=:~~~=~+++++++++++,~???++++?=+?++??++++?~~?~??==?~:~~=====~=+:=~,++?+??===++??~==+
???III?????I?I??~+III????I??+II?I???++II,?III?I?I?????++??I?IIII??+??II???:?I77?????+?+I??IIIII~OO?I??????+?+++:~~=+++=++~===~+=++?+++==~++?++=+++??+++++===?=:,?~~===??~========~+~::==+???++==++++==?+
III?+II7+II?II?+++III?+I??I??7II?I7+++II,+IIIIIIIII?I?++???II?IIII??I+????~?IIII?III?7I???I7I7+?78I?I??I????+==?++??+=:==~+=~~~=++?++++?~=???+=??+???++?++~++=~.I~+=:~=I?~=+==~=~~+~~====?I?=+=?+===++=+
?I?I+I????II?I++?=????+I?II??II7III+?+II,?7I?II?II?II??+??III?IIII?II?I??+=+I?II?+???+?I??IIII~Z78I?I???I??++++++??I?++==+++=:~=+++?+:+++=??++??+?+++?++++==+~=,I=::==+?=~+?+++===?=~+++++I+++===+==next